Celestial Navigation for the TI-89

From the description for inac:

Astnav89/INAC, Implementation of Navigational Algorithms in Computers. This program will take in sextant readings and put out your latitude and longitude. (...) It also has a planetarium and great circle calculator, partial coastal navigation and more.

TI calculator division makes money, again

For the fourth quarter of 2005, TI's calculator division ('Educational and Productivity Solutions) made $10 million on $67 million revenue. Not bad. The complete report is here.

TI68k programs of note: Karnaugh maps and sudoku

This looks like a comprehensive Karnaugh map program for working with logic expressions.

If you're into the sudoku thing, you can now waste time just about anywhere with your calculator.

A really tiny fish

A new record has been set for the tiniest known fish. From the Yahoo News article:

"This is one of the strangest fish that I've seen in my whole career,' said Ralf Britz, a zoologist at the Natural History Museum in London. "It's tiny, it lives in acid and it has these bizarre grasping fins."

and an actual picture here.

Filename extensions for TI68k objects

TI68k objects such as variables, numbers, programs and pictures are stored as PC files with particular extensions. The table below is taken from the TI Connect application Help. In general the extension has the form .XXa, where XX specifies the calculator type and a specifies the object type. The table below shows the a codes.

a == Geometry figure
c == Complex variable
d == Graph database
e == Expression
f == Function
i == Picture
k == Application
l == List
m == Matrix
n == Number (real or complex)
p == Program
r == Lab report
s == String
t == Table device setting, or text variable
u == Operating system
w == Window settings
x == Geometry macro
y == Equation or function
z == ASM program, or window values

The calculator codes XX are

89 == TI-89
92 == TI-92, TI-92 Plus
v2 == Voyage 200

Was Columbus a pirate? 300 Catalonians donate spit to find out

From the article:

While historians have mostly assumed that Columbus was an Italian born in 1451 in Genoa, a persuasive counter-lobby argues that the mariner who pioneered the Spanish conquista was in reality the Catalan Cristofol Colom, who airbrushed his past to conceal his activities as a pirate and conspirator against the king.

Copper shortage hypothesized

Research results of a team led by Thomas Graedel of Yale are summarized in the Scientific American article Measure of Metal Supply Finds Future Shortage. Running out of copper would be bad:

In fact, residents of Canada, Mexico and the U.S. required an average of 170 kilograms of copper per person. Multiply that by overall population estimates of 10 billion people by 2100 and the world will require 1.7 billion metric tons of copper by that date--more than even the most generous estimate of available resources.

The analysis seems thoughtful and conservative.

TI 68K graphing anomalies

This is not a new site by any means, but still a nice summary of misleading function plots. The 'false asymptote' problem has been fixed in AMS 3.10, and the 'partial circle' effect is well-known.

The most interesting example is the plot of y = x(x-5)^(2/5), in which most of the plot is missing. The complete plot is shown by expressing the function as y = x((x-5)^2)^(1/5), which avoids the intermediate complex result from (x-5)^(2/5), where x<5.

The remaining examples are not problems specific to the TI 68K calculators, but misleading effects from plotting the example functions with discrete resolution.

Rational geometry eliminates trig function calculations

This EE Times article describes a rational representation of angles with which, the system's inventor claims, all the familiar engineering calculations that currently require tables or a calculator can be done with simple arithmetic. To elaborate,

His approach drops the definition of distance, which requires the use of square roots, and instead uses the unit he calls quadrance, which compensates for irrational numbers by squaring all distances. Wildberger's second innovation is to define a degree of spread between two intersecting lines by using quadrances instead of angles. Combining quadrances and spreads, in place of distance and angles, yields rational trigonometry.

An Introduction to Different Rounding Algorithms

This article at the Programmable Logic Design website describes most rounding possibilities. The second part of the article is several simulations of rounding applied to a digital filter implementation which demonstrate the bias resulting from the rounding methods. Unfortunately the examples don't show the errors that can result from hundreds or thousands of operations, which is where the problem really gets serious.

Writing very reliable software

Here's an article in IEEE Spectrum about Praxis, a British firm specializing in extremely high reliablity software. The interesting features about their development approach are that they spend a lot of time up-front writing a requirements specification, implementing the software first in Z, a formal predicate languange so the code can be mathematically proven correct, and finally doing the actual coding in Sparks, a language derived from Ada. Ada, in turn was designed from the start to write reliable code.

TI sells sensors business unit, noncommital about calculators

This article at Computer Business Review Online is one of hundreds on the sale of TI's sensor unit. But this one also includes a snippet on the calculator business:

Meanwhile, TI VP and investor relations manager Ron Slaymaker would not say whether the company would follow up the S&C sale with the disposal of another fringe activity, its calculator business, which generates about 5% of revenue. However, he did point out that it is highly profitable, with margins of more than 40%.

Most calculator users, being students and not working engineers, seem unaware that calculators are a tiny part of TI's business, compared with seminconductors. It is interesting to imagine what would happen if TI did sell the calculator business, though. Who would buy it? Maybe Casio, maybe HP? I doubt that HP would put the money into it. Whoever did buy it would get a nice batch of patents, although those patents don't seem to prevent what little innovation there is in calculator design.

Three crises in mathematics

Brian Davies' makes the argument in his paper Whither Mathematics that


... developments of the classical Greek view of mathematics do not adequately represent current trends in the subject. It proved remarkably successful for many centuries, but three crises in the twentieth century force us to reconsider the status of an increasing amount of current mathematical research


The three crises stem from Godel's Incompleteness Theorem and proofs which are too long and complex for mathematicians to be confident that they are actually correct. Davies also discusses a bit about the use of computers in mathematics and the formal verfication of proofs. The paper is short and very readable.

Access to the paper requires a free and simple registration.